PolyFlow: Safe and Efficient Polytope-Constrained Flow Matching with Constraint Embedding and Projection-free Update

While flow-based generative models have demonstrated strong performance across a wide range of domains, deploying them in safety-critical physical systems remains challenging due to strict constraint requirements. Existing approaches typically enforce safety through post-hoc corrections, which incur substantial computational overhead and may distort the learned distribution. We propose PolyFlow, a polytope-constrained flow matching framework that embeds constraints directly into the model and flow dynamics. PolyFlow introduces a discrete-time flow formulation and a projection-free architecture, which eliminate the discretization error and guarantee strict satisfaction of arbitrary polyhedral constraints, without the need for expensive iterative solvers. Experimental results show that PolyFlow achieves zero constraint violation while maintaining high distributional fidelity across a range of planning and control tasks. Compared to state-of-the-art constrained generation baselines, PolyFlow significantly reduces inference latency and demonstrates a favorable trade-off between safety, efficiency, and generative quality. Code is available on https://github.com/MJianM/PolyFlow.

Terrain-adaptive Central Pattern Generators with Reinforcement Learning for Hexapod Locomotion

Inspired by biological motion generation, central pattern generators (CPGs) is frequently employed in legged robot locomotion control to produce natural gait pattern with low-dimensional control signals. However, the limited adaptability and stability over complex terrains hinder its application. To address this issue, this paper proposes a terrain-adaptive locomotion control method that incorporates deep reinforcement learning (DRL) framework into CPG, where the CPG model is responsible for the generation of synchronized signals, providing basic locomotion gait, while DRL is integrated to enhance the adaptability of robot towards uneven terrains by adjusting the parameters of CPG mapping functions. The experiments conducted on the hexapod robot in Isaac Gym simulation environment demonstrated the superiority of the proposed method in terrain-adaptability, convergence rate and reward design complexity.